The present invention provides methods for determining the presence of immobilized nucleic acid employing unsymmetrical cyanine dyes that are derivatives of thiazole orange, a staining solution and select fluorogenic compounds that are characterized as being essentially non-genotoxic. The methods comprise immobilizing nucleic acid, single or double stranded DNA, RNA or a combination thereof, on a solid or semi solid support, contacting the immobilized nucleic acid with an unsymmetrical cyanine dye compound and then illuminating the immobilized nucleic acid with an appropriate wavelength whereby the presence of the nucleic acid is determined. The cyanine dye compounds are typically present in an aqueous staining solution comprising the dye compound and a tris acetate or tris borate buffer wherein the solution facilitates the contact of the dye compound and the immobilized nucleic acid. Typically the solid or semi-solid support is selected from the group consisting of a polymeric gel, a membrane, an array, a glass bead, a glass slide, and a polymeric microparticle. Preferably, the polymeric gel is agarose or polyacrylamide. The methods employing the non-genotoxic compounds represent an improvement over commonly used methods employing ethidium bromide wherein the present methods retain the advantages of ethidium bromide, ease of use and low cost, but without the disadvantageous, known mutagen requiring special handling and waste procedures.